I worked for a loooong time in a medium size development company (about 200 developers, mostly doing large web portals). My team was some kind of central DevOps in charge of architectures, cloud, technology stacks... we were ALWAYS involved in EVERY deployment, and we were directly in full charge of the big ones.
After many years of constant work alongside the DEV/QA teams my team had gotten REALLY good doing deployments (we mostly sailed on each of them, since all was well tested, prepared and automated), and the project leaders simply trusted us. In the scarce occasions we said "sorry, this is not ready for prod" they knew it was true and didn't pressured us. And our customers were happy, since needing a rollback was EXTREMELY rare.
One of the most important things we managed to agreed with all the team leaders:
Fridays are read only.
No, that doesn't means we all can go home: Friday is now "Documentation Day".
Of course, if shit hits the fan, we are ALWAYS ready to deploy fixes.
I think in about 10 years I only had one call on a weekend.